Solve (2x - 3)(5x - 1) - (2x - 3)(x - 1) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(2x-3)(5x-1)-(2x-3)(x-1)$$

Evaluate

$4x\left(2x-3\right)$

Solution Steps

Apply the distributive property by multiplying each term of $2x-3$ by each term of $5x-1$.

$$10x^{2}-2x-15x+3-\left(2x-3\right)\left(x-1\right)$$

Combine $-2x$ and $-15x$ to get $-17x$.

$$10x^{2}-17x+3-\left(2x-3\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of $2x-3$ by each term of $x-1$.

$$10x^{2}-17x+3-\left(2x^{2}-2x-3x+3\right)$$

Combine $-2x$ and $-3x$ to get $-5x$.

$$10x^{2}-17x+3-\left(2x^{2}-5x+3\right)$$

To find the opposite of $2x^{2}-5x+3$, find the opposite of each term.

$$10x^{2}-17x+3-2x^{2}-\left(-5x\right)-3$$

The opposite of $-5x$ is $5x$.

$$10x^{2}-17x+3-2x^{2}+5x-3$$

Combine $10x^{2}$ and $-2x^{2}$ to get $8x^{2}$.

$$8x^{2}-17x+3+5x-3$$

Combine $-17x$ and $5x$ to get $-12x$.

$$8x^{2}-12x+3-3$$

Subtract $3$ from $3$ to get $0$.

$$8x^{2}-12x$$

Expand

$8x^{2}-12x$

Solution Steps

Apply the distributive property by multiplying each term of $2x-3$ by each term of $5x-1$.

$$10x^{2}-2x-15x+3-\left(2x-3\right)\left(x-1\right)$$

Combine $-2x$ and $-15x$ to get $-17x$.

$$10x^{2}-17x+3-\left(2x-3\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of $2x-3$ by each term of $x-1$.

$$10x^{2}-17x+3-\left(2x^{2}-2x-3x+3\right)$$

Combine $-2x$ and $-3x$ to get $-5x$.

$$10x^{2}-17x+3-\left(2x^{2}-5x+3\right)$$

To find the opposite of $2x^{2}-5x+3$, find the opposite of each term.

$$10x^{2}-17x+3-2x^{2}-\left(-5x\right)-3$$

The opposite of $-5x$ is $5x$.

$$10x^{2}-17x+3-2x^{2}+5x-3$$

Combine $10x^{2}$ and $-2x^{2}$ to get $8x^{2}$.

$$8x^{2}-17x+3+5x-3$$

Combine $-17x$ and $5x$ to get $-12x$.

$$8x^{2}-12x+3-3$$

Subtract $3$ from $3$ to get $0$.

$$8x^{2}-12x$$